The distance from a point (m, n) to the line Ax + By + C = 0 is given by:

If the line is y = 7, that is, y - 7 = 0 the distance is:

d = |1*n - 7|/√1^2

d^2 = (n - 7)^2

The distance from (m, n) to (-2, 3) is:

d^2 = (m+2)^2 + (n-3)^2

Now we have

(n - 7)^2 = (m+2)^2 + (n-3)^2

by simplifying the above expression we get:

-8n - m^2 - 4m + 36 = 0

Since (m, n) is any point from the line, instead of m we can put x, and instead of n we can put y and get:

-8y - x^2 - 4x + 36 = 0

y = -(1/8)(x + 2)^2 + 5

The function to represent the set of all points equidistant from the point (-2, 3) and the line y=7 is the parabola:

y = -(1/8)(x + 2)^2 + 5

click here to see the graph